A196574 - OEIS

%I #8 May 09 2018 08:17:04

%S 1,7,37,145,971,4787,24837,134167,700787,3689127,19500651,102652203,

%T 541025795,2852510953,15032123527,79230081799,417611039473,

%U 2201042540865,11601003412043,61145318600329,322275993958125,1698611779257449

%N Number of n X 4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,2,3,0,4 for x=0,1,2,3,4.

%C Every 0 is next to 0 1's, every 1 is next to 1 2's, every 2 is next to 2 3's, every 3 is next to 3 0's, every 4 is next to 4 4's.

%C Column 4 of A196578.

%H R. H. Hardin, <a href="/A196574/b196574.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) +9*a(n-2) +39*a(n-3) +20*a(n-4) +12*a(n-5) +32*a(n-6) -17*a(n-7) +a(n-8) -4*a(n-9) +a(n-10).

%F Empirical g.f.: x*(1 + 5*x + 14*x^2 - 31*x^3 + 55*x^4 - 55*x^5 + 13*x^6 - 10*x^7 + x^8 + x^9) / (1 - 2*x - 9*x^2 - 39*x^3 - 20*x^4 - 12*x^5 - 32*x^6 + 17*x^7 - x^8 + 4*x^9 - x^10). - _Colin Barker_, May 09 2018

%e Some solutions for n=5:

%e ..0..0..0..0....0..0..3..0....0..3..0..0....0..0..0..0....0..0..3..0

%e ..0..3..0..0....3..0..0..3....0..0..0..0....0..0..0..3....0..0..0..0

%e ..0..3..0..0....0..0..0..0....0..3..3..0....0..3..2..0....0..0..0..0

%e ..0..0..0..0....0..0..0..3....3..0..0..0....0..0..3..0....0..0..0..0

%e ..0..3..0..0....0..0..0..0....0..3..0..0....0..3..0..0....0..0..0..0

%Y Cf. A196578.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 04 2011